enrichment factor, \(S\)

in liquid-liquid distribution
https://doi.org/10.1351/goldbook.E02127
The factor by which the ratio of two substances in the feed must be multiplied to give their ratio after treatment. \[\frac{Q_{\text{A}}}{Q_{\text{B}}} = S_{\text{A,B}}\ \frac{Q_{\text{A}}^{'}}{Q_{\text{B}}^{'}}\] where QA and QA' are the final and initial amounts of species A and QB and QB' are the final and initial amounts of species B. Hence S A,B = E A E B where E is the fraction extracted. In terms of D,n,r (where n is the number of stages and r the phase ratio), \[S_{\text{A,B}} = \frac{1- (1\,+\,r\ D_{\text{A}})^{-n}}{1- (1\,+\,r\ D_{\text{B}})^{-n}}\]
Sources:
Orange Book, 2nd ed., p. 90 (http://media.iupac.org/publications/analytical_compendium/)
PAC, 1993, 65, 2373. 'Nomenclature for liquid-liquid distribution (solvent extraction) (IUPAC Recommendations 1993)' on page 2382 (https://doi.org/10.1351/pac199365112373)